Related papers: Stable distributions
Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.
Rapidly decreasing tempered stable distributions are useful models for financial applications. However, there has been no exact method for simulation available in the literature. We remedy this by introducing an exact simulation method in…
This paper demonstrates some connections between the coefficients of a Taylor series $f(z)=\ds\sum_{n=0}^\infty a_n z^n$ and singularities of the function. There are many known results of this type, for example, counting the number of poles…
This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Failure of the main argument for the use of heavy tailed distribution in Finance is given. More precisely, one cannot observe so many outliers for Cauchy or for symmetric stable distributions as we have in reality. keywords:outliers;…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
The family of stable distributions received extensive applications in many fields of studies since it incorporates both the skewness and heavy tails. In this paper, we introduce a package written in the R language called alphastable. The…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
We establish multidimensional analogues of one-dimensional stable limit theorems due to H\"ausler and Luschgy (2015) for so called explosive processes. As special cases we present multidimensional stable limit theorems involving…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and…